1 // Copyright 2017 Google Inc. All rights reserved. 2 // 3 // Licensed under the Apache License, Version 2.0 (the "License"); 4 // you may not use this file except in compliance with the License. 5 // You may obtain a copy of the License at 6 // 7 // http://www.apache.org/licenses/LICENSE-2.0 8 // 9 // Unless required by applicable law or agreed to in writing, software 10 // distributed under the License is distributed on an "AS IS" BASIS, 11 // WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. 12 // See the License for the specific language governing permissions and 13 // limitations under the License. 14 15 package s2 16 17 // WedgeRel enumerates the possible relation between two wedges A and B. 18 type WedgeRel int 19 20 // Define the different possible relationships between two wedges. 21 // 22 // Given an edge chain (x0, x1, x2), the wedge at x1 is the region to the 23 // left of the edges. More precisely, it is the set of all rays from x1x0 24 // (inclusive) to x1x2 (exclusive) in the *clockwise* direction. 25 const ( 26 WedgeEquals WedgeRel = iota // A and B are equal. 27 WedgeProperlyContains // A is a strict superset of B. 28 WedgeIsProperlyContained // A is a strict subset of B. 29 WedgeProperlyOverlaps // A-B, B-A, and A intersect B are non-empty. 30 WedgeIsDisjoint // A and B are disjoint. 31 ) 32 33 // WedgeRelation reports the relation between two non-empty wedges 34 // A=(a0, ab1, a2) and B=(b0, ab1, b2). 35 func WedgeRelation(a0, ab1, a2, b0, b2 Point) WedgeRel { 36 // There are 6 possible edge orderings at a shared vertex (all 37 // of these orderings are circular, i.e. abcd == bcda): 38 // 39 // (1) a2 b2 b0 a0: A contains B 40 // (2) a2 a0 b0 b2: B contains A 41 // (3) a2 a0 b2 b0: A and B are disjoint 42 // (4) a2 b0 a0 b2: A and B intersect in one wedge 43 // (5) a2 b2 a0 b0: A and B intersect in one wedge 44 // (6) a2 b0 b2 a0: A and B intersect in two wedges 45 // 46 // We do not distinguish between 4, 5, and 6. 47 // We pay extra attention when some of the edges overlap. When edges 48 // overlap, several of these orderings can be satisfied, and we take 49 // the most specific. 50 if a0 == b0 && a2 == b2 { 51 return WedgeEquals 52 } 53 54 // Cases 1, 2, 5, and 6 55 if OrderedCCW(a0, a2, b2, ab1) { 56 // The cases with this vertex ordering are 1, 5, and 6, 57 if OrderedCCW(b2, b0, a0, ab1) { 58 return WedgeProperlyContains 59 } 60 61 // We are in case 5 or 6, or case 2 if a2 == b2. 62 if a2 == b2 { 63 return WedgeIsProperlyContained 64 } 65 return WedgeProperlyOverlaps 66 67 } 68 // We are in case 2, 3, or 4. 69 if OrderedCCW(a0, b0, b2, ab1) { 70 return WedgeIsProperlyContained 71 } 72 73 if OrderedCCW(a0, b0, a2, ab1) { 74 return WedgeIsDisjoint 75 } 76 return WedgeProperlyOverlaps 77 } 78 79 // WedgeContains reports whether non-empty wedge A=(a0, ab1, a2) contains B=(b0, ab1, b2). 80 // Equivalent to WedgeRelation == WedgeProperlyContains || WedgeEquals. 81 func WedgeContains(a0, ab1, a2, b0, b2 Point) bool { 82 // For A to contain B (where each loop interior is defined to be its left 83 // side), the CCW edge order around ab1 must be a2 b2 b0 a0. We split 84 // this test into two parts that test three vertices each. 85 return OrderedCCW(a2, b2, b0, ab1) && OrderedCCW(b0, a0, a2, ab1) 86 } 87 88 // WedgeIntersects reports whether non-empty wedge A=(a0, ab1, a2) intersects B=(b0, ab1, b2). 89 // Equivalent but faster than WedgeRelation != WedgeIsDisjoint 90 func WedgeIntersects(a0, ab1, a2, b0, b2 Point) bool { 91 // For A not to intersect B (where each loop interior is defined to be 92 // its left side), the CCW edge order around ab1 must be a0 b2 b0 a2. 93 // Note that it's important to write these conditions as negatives 94 // (!OrderedCCW(a,b,c,o) rather than Ordered(c,b,a,o)) to get correct 95 // results when two vertices are the same. 96 return !(OrderedCCW(a0, b2, b0, ab1) && OrderedCCW(b0, a2, a0, ab1)) 97 } 98